Computational modelling of the flow and heat transfer in an idealized porous metal

Metallic foams with an inter-connected void phase have a large available internal surface area that can be used instead of formed extended fins for heat transfer applications. To investigate the feasibility of the use of metallic foams in heat transfer applications, models for heat transfer and pressure drop for this type of porous materials are developed. This can not be done without a close observation of the pore-level flow structure.;A thermal periodic boundary condition is developed to compute heat transfer in spatially periodic domains. The condition is formulated on the basis of thermal similarity and is implemented within the framework of a mass flow-based periodic condition for the flow field. The thermal periodic boundary condition is validated by computing the flow and heat transfer for fully-developed pipe flow under constant heat flux and constant wall temperature conditions, and for a generic spatially-periodic geometry.;The periodic boundary condition is implemented in the three-dimensional code and numerical simulations are performed over a range of idealized pore geometries. A semiheuristic model is developed for pressure drop using Carman-Kozeny theory and an Ergun-like quadratic extension is added to the model for higher Reynolds number regimes. Verification of the model using the results of the simulations revealed that the main characteristic pore-level length-scale is the pore-window diameter of the inter-connected void phase. The variation of the resulting Kozeny constant is consistent with that reported in literature for other types of pore geometry. Moreover, the presence of a cubic behavior of pressure drop in temrs of velocity in the weak inertia flow regime was explored and observed, which was in agreement with the theory of weak inertia flow in existing literature. A heat transfer model is developed using parametric study on the data from the simulations. The model shows that the characteristic pore-level length-scale for heat transfer is the pore diameter. The proposed models can be used as outlines for future experimental studies.;Keywords: finite-volume method; parallel computing; unstructured grid; incompressible flow; peridoc boundary condition; metallic foam; porous media; heat transfer;In this work, numerical simulations are carried out for laminar periodic, thermofluid flow in an idealized pore geometry of metallic foams with a wide range of geometry parameters. With the guidance of theoretical analysis, semiheuristic models for pressure drop and heat transfer are developed from the results of simulation. To this end, a parallel code is developed to solve three-dimensional, laminar flow and heat transfer using an unstructured finite-volume method. The discretization, parallelization and performance of the implicit, unstructured, time-dependent Computational Fluid Dynamics code is described. A detailed description is provided of the improvements made on second-order accurate tools for spatial interpolation and gradient calculation to discretize the Navier-Stokes equations in an unstructured framework. The main goal in the development of the discretization tools was to ensure a scalable and accurate parallel code. The performance of the discretization tools has been validated using standard bench-mark problems for non-uniform, non-orthogonal grids. Parallelisation of the code is done within the PETSc (Portable, Extensible Toolkit for Scientific Computation) framework using a single-program-multiple-data (SPMD) parallelization model. The resulting parallel code is shown to scale linearly within the limit of the available number of processors.